And I'll bet you never read my original post. I called multiple times to have the box activated (and reset).
Your post was confusing with both your connection with a splitter, tv ch 3/4 and DTA-HDMI connection. You may have unuseable levels with a splitter in line.
The TV's HDMI firmware may be whacked. (thanks to HDCP/ Cec/ARC errors)
What did TWC tell you when they were done? They may be able to tell what type of TV is connected via HDMI and possibly the set got an upgrade to handle that version box.
On all but DTA's, they have a 2 way communications path to your box. Was the box ever replaced with a new one?
This is peer to peerr support, we don't have a clue why TWC does what they do...
You would not be doing a search on the TV for channels the cable box would be the tuner, not the TV set. You want to use the Cable box, whether it be a DTA or a Set Top Box to change channels. As it was said, you switch the TV to the Input that the cable box is connected to the TV with and use the cable box remote to switch channels.
If you are still having trouble after that please do let us know.
^TWC-Social Media Customer Care
OP had both devices connected thru a splitter per the original post, unknown if that tv decodes clear qam and if there are any clear qam channels on his head end or there are a couple NTSC analogs like for local govt/ public access channels.